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Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer

Published online by Cambridge University Press:  05 November 2015

K. E. BOUTARENE  and
P.-H. COCQUET
K. E. BOUTARENE
Affiliation:
USTHB, Faculty of Mathematics, AMNEDP Laboratory, PO Box 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria email: [email protected]
P.-H. COCQUET
Affiliation:
Laboratory of Physics and Mathematical Engineering for Energy and the Environment (PIMENT), University of La Réunion, 2 rue Joseph Wetzell, 97490 Sainte-Clotilde, France email: [email protected]
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Abstract

This work looks at the asymptotic behaviour of the solution to the Helmholtz equation in a penetrable domain of $\mathbb{R}$3 with a thin layer of thickness δ which tends to 0. We use the method of multi-scale expansion to derive and justify an asymptotic expansion of the solution with respect to the thickness δ up to any order. We then provide approximate transmission conditions of order two defined on an interface located inside the thin layer, with accuracy up to O(δ2), which allow one to take into account the influence of the thin layer.

Keywords

Asymptotic analysisAsymptotic expansionsWave scatteringHelmholtz equationThin structures
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 2 , April 2016 , pp. 264 - 310
Copyright
Copyright © Cambridge University Press 2015 

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